Determine whether the following trajectory lies on either a circle in R 3 or a sphere...

 

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Determine whether the following trajectory lies on either a circle in R² 3 or a sphere in R³ centered at the origin. If so, find the radius of the circle or sphere, and show that the position vector and the velocity vector are everywhere orthogonal. r(t)=(6 cos 2t,6 sin 2t), for 0≤t≤ Determine whether the following trajectory lies on either a circle in R² or a sphere in R³ centered at the origin. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The trajectory lies on a sphere with radius (Simplify your answer.) ○ B. The trajectory lies on a circle with radius (Simplify your answer.) C. The trajectory does not lie on a circle or a sphere. Show that the position vector and the velocity vector are everywhere orthogonal. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Since r⚫v= (Type exact answers.) (- 12 sin (2t)) + (6 sin 2t) ( ) for 0≤t≤л, the position vector r and velocity vector v are orthogonal. , the position vector r and velocity vector V are orthogonal. OB. Since r⚫v= = ( ) (0) + (0)( ) (Type integers or decimals.) C. Since rxv= = ( _,6) × (0, (Type integers or decimals.) the position vector r and velocity vector v are orthogonal. D. Since rxv= ,6 sin 2t) x ( -12 sin (2t), (Type exact answers.) = for 0≤ts, the position vector r and velocity vector V are orthogonal. ○ E. The trajectory does not lie on a circle or a sphere. Determine whether the following trajectory lies on either a circle in R² 3 or a sphere in R³ centered at the origin. If so, find the radius of the circle or sphere, and show that the position vector and the velocity vector are everywhere orthogonal. r(t)=(6 cos 2t,6 sin 2t), for 0≤t≤ Determine whether the following trajectory lies on either a circle in R² or a sphere in R³ centered at the origin. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The trajectory lies on a sphere with radius (Simplify your answer.) ○ B. The trajectory lies on a circle with radius (Simplify your answer.) C. The trajectory does not lie on a circle or a sphere. Show that the position vector and the velocity vector are everywhere orthogonal. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Since r⚫v= (Type exact answers.) (- 12 sin (2t)) + (6 sin 2t) ( ) for 0≤t≤л, the position vector r and velocity vector v are orthogonal. , the position vector r and velocity vector V are orthogonal. OB. Since r⚫v= = ( ) (0) + (0)( ) (Type integers or decimals.) C. Since rxv= = ( _,6) × (0, (Type integers or decimals.) the position vector r and velocity vector v are orthogonal. D. Since rxv= ,6 sin 2t) x ( -12 sin (2t), (Type exact answers.) = for 0≤ts, the position vector r and velocity vector V are orthogonal. ○ E. The trajectory does not lie on a circle or a sphere.

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